The hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle.The shorter side of the triangle is 7 centimeters...

Let the sides be x, y and the hypotenuse
h.

Given that h is 2 more than the longer
sides.

Let the longer side be
x.

==> h =
x+2...............(1)

The shorter side (y) is 7 less than
the longer sides.

==> y= x-7
..............(2)

But we know that
L

h^2 = x^2 + y^2

==>
(x+2)^2 = x^2 + (x-7)^2

==> x^2 + 4x +4 = x^2 + x^2
-14x + 49

==> x^2 + 4x +4 = 2x^2 -14x +
49

==> x^2 -18x + 45 =
0

==> (x-3)(x-15) =
0

==> x1= 3 ==> y= 3-7 = -4
(impossible)

==> x2=15 ==> y2= 15-7 =
8

==> h= 15+2 =
17

Then, the length of the hypotenuse is 17
cm.